There are a couple books that I can think of that might be of use to you for this. First, there is Ian Wood's The Merovingian Kingdoms, 450-751 in which he focuses a lot on the continuities between the Roman Empire and the successor states after the collapse of the empire. He mainly approaches this through the lens of literary continuity and some political continuity. So definitely a good place to start.
Another good book would be the collection of essays edited by Jennifer Davis and Michael McCormick called The Long Morning of Medieval Europe which I have not read completely, but the theme of reevaluating the early middle ages is pretty common throughout.
If you have any specific things you would be interested in let me know!
Not a book, but I recently watched the videos and read some of the sources for this online course from yale: http://oyc.yale.edu/history/hist-210
The videos are all free to watch (on youtube), and the content is very interesting on this topic. It's a pretty heavy investment though (over 20 hour-long lectures) but it was definitely worth watching.
On top of the other suggestions mentioned, Chris Wickham's The Inheritance of Rome is a great introduction to the period for non-specialists. The primary focus is the 'heirs' to the Roman Empire of Antiquity (the Eastern Roman Empire, the 'Barbarian' Kingdoms, the Church, and the Caliphate) from 400-1000. It's a good place to start if you want to get a broad sense for what was happening in Europe and the Mediterranean world.
There are several good posts dealing with that in the FAQ, I'd recommend checking out the books the top level comments of those posts cited.
Pernoud, ReĢgine. 2000. Those terrible Middle Ages: debunking the myths. San Francisco: Ignatius Press.
A French historian offers an easy to read, engaging take on the prevailing myths about the Middle Ages and what the evidence actually supports. It's not meant as a formal monograph so much as a polemical rebuttal of popular misconceptions, but for a non-expert in that subject (like me) it was a great start.